Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x+8y &= 8 \\ -3x-y &= -6\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-y = 3x-6$ Divide both sides by $-1$ to isolate $y$ $y = {-3x + 6}$ Substitute this expression for $y$ in the first equation. $4x+8({-3x + 6}) = 8$ $4x - 24x + 48 = 8$ Simplify by combining terms, then solve for $x$ $-20x + 48 = 8$ $-20x = -40$ $x = 2$ Substitute $2$ for $x$ back into the top equation. $4( 2)+8y = 8$ $8+8y = 8$ $8y = 0$ $y = 0$ The solution is $\enspace x = 2, \enspace y = 0$.